# Surfaces and Gradients

Surfaces and Gradients

Visualize how gradients relate to surfaces.

The points satisfying for a particular value of form the surface shown. As varies, the surface deforms along the normals defined by the vector field , the gradient of , represented by the arrows.

(x,y,z)

w=f(x,y,z)=u+v+

2

x

2

y

2

z

w

w

∇f=++

∂f

∂x

i

∂f

∂y

j

∂f

∂z

k

f

Due to the complex nature of this Demonstration, there may be a delay between changing the variables and updating the graph.